An “Ageing” Operator and Its Use in the Highly Constrained
Topological Optimization of HVAC System Design
Jonathan Wight, Yi Zhang
Department of Civil and Building Engineering, Loughborough University,
LE11 3TU, UK
The synthesis of novel heating, ventilating, and air-conditioning
(HVAC), system configurations is a mixed-integer, non-linear,
highly constrained, multi-modal, optimization problem, with
many of the constraints being subject to time-varying boundary
conditions on the system operation. It was observed that the
highly constrained nature of the problem resulted in the
dominance of the search by a single topology. This paper,
introduces an new evolutionary algorithm operator that prevents
topology dominance by penalizing solutions that have a dominant
The operator results in a range of dynamic behavior for the rates
of growth in topology dominance. Similarly, the application of
the ageing penalty can result in the attenuation of topology
dominance, or more severely, the complete removal of a topology
from the search. It was also observed that following the
penalization of a dominant topology, the search was dynamically
re-seeded with both new and previously evaluated topologies. It is
concluded that the operator prevents topology dominance and
increases the exploratory power of the algorithm.
The application of an evolutionary algorithm with ageing to the
synthesis of HVAC system configurations resulted in a novel
design solution having a 15% lower energy use than the best of
conventional system designs.
Categories and Subject Descriptors
I.2.8 [Artificial Intelligence]: Problem Solving, Control
Methods, and Search – heuristic methods.
J.6 [Computer-Aided Engineering]: Computer-aided Design
General Terms: Algorithms, Design.
Keywords: Evolutionary Algorithms, Topological
Optimization, HVAC, System Design.
The temperature and humidity of the air in the occupied spaces of
commercial buildings, is maintained by “heating, ventilating and
air conditioning” (HVAC), systems. HVAC systems ventilate
buildings by taking in outside air and mixing it with air that has
been re-circulated from within the building. The ventilation air is
further conditioned by heating, cooling, and humidifying
components. The ventilation air maintains the room temperature
and humidity by being supplied to the room at a condition that
offsets thermal loads on the room.
The air conditioning components can be connected together in a
number of ways to produce a viable system configuration. Over
the last 100 years, a number of recognized configurations have
evolved through the process of heuristic design . The
alternative design solutions have been driven predominantly by
the need to limit the capital cost of the systems. This has led to
system configurations that are able to maintain the temperature
and humidity in more than one “control zone” (a control zone
being a collection of rooms that experience similar heat loads).
However, many of the established “multi-zone” systems have a
higher than necessary energy consumption (a “multi-zone” system
is one that simultaneously conditions more than one control
Concerns over climate change and associated energy use has
renewed interest in the design of HVAC systems for low energy
use. This paper describe an approach to the automatic synthesis of
HVAC system configurations for minimum energy use by an
evolutionary algorithm. A new algorithm operator which is
designed to maintain the power of the search in exploring
alternative system topologies is also described.
1.1 Problem Characteristics and
There are three elements to the design of an HVAC system,
the selection of a component set (the choice of type and
number of components);
given the component set, the design of the feasible
optimization of the system operation (for several
different operating conditions).
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The selection of a feasible topology is dependent on the
component set and similarly, the optimization of system operation
whereas those that exceed the limit are penalized. It was
concluded that the ageing operator:
prevents the long term dominance of the search by any one
exhibits a variety of different dynamic behaviors in terms of
the growth in dominance and its penalization; these range
from long slow growth and weak penalization over many
generations, to rapid growth in dominance with a
correspondingly severe penalization of solutions;
and exhibits a dynamic behavior in the re-seeding of the
population with new and previously searched topologies;
increases the number of topologies searched;
requires further research to investigate the effect of the
ageing limit parameter on the dynamic behavior of the
It was demonstrated that the application of the ageing operator
increases the probability of finding a feasible solution from 28%
to 66% (the example problem being highly constrained). It was
concluded that the cause of infeasibility was due to the search
being unable to solve one or more of the equality constraints on
the zone temperature and humidity. Given that these constraints
are dependent on the boundary conditions on the system
operation, and that the system operation is represented by a
separate chromosome for each boundary condition, it is concluded
that the effectiveness of the algorithm may be improved through
the application of chromosome specific selection and
recombination, the selection and recombination being a function
of sub-fitness at a particular boundary condition (in a similar
manner to that reported in [4,6]).
It was also demonstrated that the introduction of the ageing
operator, resulted in a statistically significant improvement in the
feasible objective function values found by the evolutionary
algorithm. In particular, the system configuration for the best
solution found when using the ageing operator, had novel features
that enabled it to operate with a 15% lower energy use than the
best of the conventional systems (this being considered a
significant achievement, as the established systems are a result of
over a century of engineering research and development).
It can be concluded that the ageing operator had a significant
impact on the performance of the evolutionary algorithm in
solving this highly constrained topological optimization problem,
and the best solution found by the search represented a novel
design having a significantly better performance than established
This work was funded by the American Society of Heating,
Refrigerating, and Air-Conditioning Engineers (ASHRAE), under
research project RP-1049.
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